Planar and Poly-Arc Lombardi Drawings
Christian A. Duncan, David Eppstein, Michael T. Goodrich, Stephen Kobourov, Maarten Löffler, Nöllenburg, Martin · Journal of Computational Geometry (Carleton University) · 2011
In Lombardi drawings of graphs, edges are represented as circular arcs, and the edges incident on vertices have perfect angular resolution. However, not every graph has a Lombardi drawing, and not every planar graph has a planar Lombardi drawing. We introduce k-Lombardi drawings, in which each edge may be drawn with k circular arcs, noting that every graph has a smooth 2-Lombardi drawing. We show that every planar graph has a smooth planar 3-Lombardi drawing and further investigate topics connecting planarity and Lombardi drawings.